I´m trying to prove that $$ f(x)= \left\{ \begin{array}{lcc} 1-\sqrt{1-4p(1-p)s^2}& if & 0 \leq s < 1\\ \\ 1 & if& s=1 \end{array} \right. $$ is a generating function of a distribution with $p \in [0,1] $.
I´m trying to use the binomial theorem but I can´t solve it. Someone could help me to prove that this is a generating function of a distribution pls.
Thanks for your time and help.